In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the difference between the product of empirical characteristic functions and some constant. Special attention is given to the case of testing univariate normality in which we derive the test statistic explicitly in terms of Bessel function, and the case of testing bivariate normality and independence. The tests show quality performance in comparison to some popular powerful competitors.

翻译：在本条中,我们证明艾兹蒙特对多种变式正常分布的定性是泛泛化的,我们在此基础上提出了关于独立性和正常性的新检验标准。测试使用了经验特性函数和某种常数之间差异的平方模量。我们特别注意的是测试单向正常性的情况,我们从贝瑟尔功能和双向正常性和独立性的检验中明确得出测试统计数据。测试表明,与一些流行的强势竞争者相比,测试质量表现。